AnswersFL-1200710-Mathematics for College Algebra AModeling with Systems of Linear Equations

Exponential Decay Functions Answers

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Terrence buys a new car for $20,000. The value of the car depreciates by 15% each year. If f(x) represents the value of the car after x years, which function represents the car’s value?

A
f(x) = 20,000(0.85)x
B
f(x) = 20,000(0.15)x
C
f(x) = 20,000(1.15)x
D
f(x) = 20,000(1.85)x
2
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Ginny is studying a population of frogs. She determines that the population is decreasing at an average rate of 3% per year. When she began her study, the frog population was estimated at 1,200. Which function represents the frog population after x years?

A
f(x) = 1,200(1.03)x
B
f(x) = 1,200(0.03)x
C
f(x) = 1,200(0.97)x
D
f(x) = 1,200(0.97x)
3

Two exponential functions are shown in the table.

Question illustration
A
The functions f(x) and g(x) are reflections over the x-axis.
B
The functions f(x) and g(x) are reflections over the y-axis.
C
The function f(x) is a decreasing function, and g(x) is an increasing function.
D
The function f(x) has a greater initial value than g(x).
4

Hal is asked to write an exponential function to represent the value of a $10,000 investment decreasing at 2% annually. What multiplicative rate of change should Hal use in his function?

A
0.02
B
0.98
C
1.02
D
1.98
5

The graph of f(x) = 2x is shown on the grid.

Question illustration
A
On a coordinate plane, an exponential function approaches x = 0 in quadrant 4 and increases into quadrant 1.
Option A
B
On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0.
Option B
C
On a coordinate plane, an exponential function approaches y = 0 in quadrant 3 and curves down into quadrant 4.
Option C
D
On a coordinate plane, an exponential function approaches x = 0 in quadrant 1 and curves down and to the right into quadrant 4.
Option D
6

Which is the graph of f(x) = 100(0.7)x?

A
On a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up into quadrant 2. It goes through (2, 49) and (0, 100).
Option A
B
On a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up into quadrant 2. It goes through (2, 9) and (0, 100).
Option B
C
On a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up into quadrant 2. It goes through (2, 70) and (0, 100).
Option C
D
On a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up into quadrant 2. It goes through (2, 30) and (0, 100).
Option D
7

What is the multiplicative rate of change for the exponential function f(x) = ?

Question illustration
A
0.4
B
0.6
C
1.5
D
2.5
8

A population of bacteria is treated with an antibiotic. It is estimated that 5,000 live bacteria existed in the sample before treatment. After each day of treatment, 40% of the sample remains alive. Which best describes the graph of the function that represents the number of live bacteria after x days of treatment?

A
f(x) = 5000(0.4)x, with a horizontal asymptote of y = 0
B
f(x) = 5000(0.6)x, with a vertical asymptote of x = 0
C
f(x) = 5000(1.4)x, with a horizontal asymptote of y = 0
D
f(x) = 5000(1.6)x, with a vertical asymptote of x = 0
9

Chelsea is graphing the function f(x) = 20()x. She begins by plotting the initial value. Which graph represents her first step?

Question illustration
A
On a coordinate plane, the point (0, 0.25) is graphed.
Option A
B
On a coordinate plane, the point (0.25, 0) is graphed.
Option B
C
On a coordinate plane, the point (0, 20) is graphed.
Option C
D
On a coordinate plane, the point (20, 0) is graphed.
Option D
10

Which is an exponential decay function?

A
f start bracket x end bracket equals Three-fourths start bracket Seven-fourths end bracket superscript x
Option A
B
f start bracket x end bracket equals two-third start bracket Four-fifths end bracket superscript negative x
Option B
C
f start bracket x end bracket equals Three-halves start bracket Eight-sevenths end bracket superscript negative x
Option C
D
f start bracket x end bracket equals one-third start bracket negative nine-halves end bracket superscript x
Option D

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